Photolithography is a process used in microfabrication to pattern the bulk of a substrate. It uses light to transfer a geometric pattern from an optical mask to a light-sensitive chemical “photoresist”, or simply “resist,” on the substrate. The pattern in the resist is created by exposing it to light with a projected image using an optical mask.
Optical proximity correction (OPC) is a photolithography enhancement technique commonly used to compensate for image errors due to diffraction or process effects. OPC corrects image errors by moving edges or adding extra polygons to the pattern written on the optical mask. Model based OPC uses compact models to dynamically simulate the final pattern and thereby derive the movement of edges, typically broken into sections, to find the best solution. The objective is to reproduce, as well as possible, the original layout drawn by the designer in the silicon wafer.
The cost of manufacturing advanced mask sets is steadily increasing as technology becomes more and more complex. In addition, the turn-around time is always an important consideration in semiconductor manufacturing. As a result, computer simulations of the photolithography process, which assist in reducing both the cost and turn-around time, have become an integral part of semiconductor manufacturing.
One of the most important inputs to any photolithography simulation system is the model for the interaction between the illuminating electric field and the mask. Conventionally, the thin mask approximation is used in most photolithography simulation systems. The thin mask approximation, also called the Kirchhoff boundary condition or mask two-dimensional (2D), assumes that the thickness of the structures on the mask is very small compared with the wavelength and that the widths of the structures on the mask are very large compared with the wavelength. Therefore, the thin mask model provides reasonably accurate calculations for feature sizes much larger than the exposure wavelength.
As semiconductor feature sizes continue to shrink further below the exposure wavelength, mask topography effect, also called thick mask effect or mask three-dimensional (3D), is a considerable factor to impact the photolithography modeling and full chip OPC process. The mask topography effect includes polarization dependence due to the different boundary conditions for the electric and magnetic fields, transmission and phase error in small openings, edge diffraction (or scattering) effects or electromagnetic coupling.
The thin mask approximation is not accurate enough in simulating mask topography effect. FIG. 1A illustrates a mask image simulated by using thin mask model. Specifically, this figure shows light 110 passes through an optical mask 105. The resulting mask image, as simulated by the thin mask model, is pattern 115.
In optical reflection, the plane of incidence is the plane spanned by the surface normal and the propagation vector of the incoming radiation. The component of the electric field parallel to the plane of incidence is termed p-like (parallel) and the component perpendicular to the plane of incidence is termed s-like. Light with a p-like electric field is said to be a transverse-magnetic (TM) wave. Light with an s-like electric field is called a transverse-electric (TE) wave.
FIG. 1B illustrates mask images rigorously simulated by using thick mask model that takes mask topography effect into consideration. Specifically, this figure shows light is decomposed into TE wave 120 and TM wave 125. The TE wave 120 and TM wave 125 pass through the optical mask 105. The resulting mask images, as rigorously simulated by the thick mask model, are patterns 130 and 135, respectively. As illustrated in FIG. 1B, both the patterns 130 and 135 have wave perturbations 150 and 155 respectively, due to the mask topography effect. The wave perturbations 150 and 155 cannot be accurately simulated by using the thin mask model described in FIG. 1A above.
Among different types of modeling schemes for tackling mask topography effect, rigorous simulation is usually considered to be accurate. But rigorous simulation runs extremely slowly, making it impractical for full chip level implementation. Instead, application of rigorous simulation is limited to small areas of a chip design layout. The prior art of the compact modeling schemes with domain decomposition and boundary layer definition lack real physical meaning and rely on intensive model fitting. Consequently, conventional compact modeling schemes cannot accurately simulate the mask topography effect. Furthermore, conventional compact modeling schemes lack flexibility for dealing with all-angle patterns.
Edge coupling effect is the mask near-field interaction among adjacent edges. In photolithography simulation, strong edge coupling effect will be generated when feature size and space are small. Prior art photolithography simulation schemes do not address edge coupling effect with both accuracy and runtime efficiency.
Off-axis illumination (OAI) is an optical system setup in which the incoming light strikes the optical mask at an oblique angle rather than perpendicularly. OAI brings additional complication to the photolithography simulation of mask topography effect.